Two-stage depth estimation machine learning algorithm and spherical warping layer for equi-rectangular projection stereo matching

ABSTRACT

A system and method is disclosed having an end-to-end two-stage depth estimation deep learning framework that takes one spherical color image and estimate dense spherical depth maps. The contemplated framework may include a view synthesis (stage 1) and a multi-view stereo matching (stage 2). The combination of the two-stage process may provide the advantage of the geometric constraints from stereo matching to improve depth map quality, without the need of additional input data. It is also contemplated that a spherical warping layer may be used to integrate multiple spherical features volumes to one cost volume with uniformly sampled inverse depth for the multi-view spherical stereo matching stage. The two-stage spherical depth estimation system and method may be used in various applications including virtual reality, autonomous driving and robotics.

TECHNICAL FIELD

The present disclosure relates to a system and method having anend-to-end two-stage depth estimation machine learning framework and aspherical warping layer for equirectangular projection stereo matching.

BACKGROUND

Three-dimensional (3D) scene understanding may be relevant forapplications like virtual reality (VR), augmented reality (AR),autonomous driving, or robotics. For example, quick and reliableacquisition of omnidirectional 3D data is considered a useful buildingblock of such applications to enable user interaction with the digitalenvironment.

SUMMARY

A system and method is disclosed for employing a two-stage depthestimation deep machine learning algorithm that comprises a first stagethat provides a equirectangular projection (ERP) image to a coarsemonocular depth estimation machine learning algorithm operable toestimate a coarse depth map. The first stage also comprising adifferentiable depth image based rendering (DIBR) algorithm thatreceives the coarse depth map and generates one or more synthesizedimages.

A second stage may provide the ERP image and the one or more synthesizedimages to a multi-view stereo matching machine learning algorithm thatincludes two cascaded stages for disparity prediction in acoarse-to-fine manor. The multi-view stereo matching machine learningalgorithm may also be operable to generate a final spherical depth map.

The second stage may include a spherical feature extraction machinelearning algorithm that pairs the one or more synthesized images withthe ERP image and generates one or more feature maps. The second stagemay also include a cost volume construction algorithm that aggregatesspherical features extracted from the ERP image and the one or moresynthesized images. The cost volume construction algorithm may alsogenerate a cost volume using a depth hypothesis that is uniformlysampled. It is contemplated the one or more feature maps may be used bythe cost volume construction algorithm to generate the cost volume. Itis also contemplated the depth hypothesis may be uniformly sampled at aspecified level using new intervals.

The second stage may further include a cost aggregation machine learningalgorithm operable to aggregate the cost volume using one or more3-dimensional convolutional neural networks. The cost aggregationmachine learning algorithm may be implemented using an hourglassencoding and decoding processes. The second stage may include aregression algorithm that regresses a disparity value pixel-wise foreach specified level. It is contemplated that the coarse depth map andthe final spherical depth map may be supervised using a ground truthdepth map.

It is also contemplated that the coarse monocular depth estimationmachine learning algorithm may be implemented as a light-weight machinelearning network that utilizes coordinate convolution to enforce360-degree awareness. The DIBR algorithm may also be operable totransform a first pixel set from the ERP image to a second pixel set ona target image in a fully differentiable manner. Lastly, the DIBRalgorithm may be operable to splat the first pixel set on the targetimage, the DIBR algorithm also including a soft z-buffering algorithm tohandle occlusions, and the DIBR algorithm may generate a finalprediction that is a weighted average of points which splat to a singlepixel from the second pixel set.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an exemplary computing system that may be used bydisclosed embodiments.

FIG. 2 illustrates an exemplary embodiment of a end-to-end two-stagedepth estimation deep learning framework.

FIG. 3 illustrates an exemplary embodiment of a multi-viewomnidirectional stereo matching network.

FIG. 4 illustrates an exemplary machine learning convolutional neuralnetwork (CNN).

FIG. 5 is an embodiment in which a computer system may be used tocontrol an automated personal assistant.

FIG. 6 illustrates a computing system controlling an at least partiallyautonomous robot.

FIG. 7 is an embodiment in which the computing system may be used tocontrol a surveillance system.

DETAILED DESCRIPTION

Embodiments of the present disclosure are described herein. It is to beunderstood, however, that the disclosed embodiments are merely examplesand other embodiments can take various and alternative forms. Thefigures are not necessarily to scale; some features could be exaggeratedor minimized to show details of particular components. Therefore,specific structural and functional details disclosed herein are not tobe interpreted as limiting, but merely as a representative basis forteaching one skilled in the art to variously employ the embodiments. Asthose of ordinary skill in the art will understand, various featuresillustrated and described with reference to any one of the figures canbe combined with features illustrated in one or more other figures toproduce embodiments that are not explicitly illustrated or described.The combinations of features illustrated provide representativeembodiments for typical applications. Various combinations andmodifications of the features consistent with the teachings of thisdisclosure, however, could be desired for particular applications orimplementations.

Machine learning algorithms (e.g., CNN or DNN) employed on sphericalimages are increasingly becoming more widely used. For instance, machinelearning algorithms are emerging in applications pertaining to deeplearning on 360-degree images. Also, equi-rectangular projection images(which may be a continuous context representation that includes mild tosevere distortion) is one known representation of omnidirectionalimages.

To improve the effectiveness of a convolutional kernel employed by amachine learning algorithm omni-depth may be used to introduce a seriesof rectangular filter banks of various kernel sizes to account forequirectangular distortions. It is also contemplated thatdistortion-aware spherical kernels derived from traditionalconvolutional kernels may also be employed. Such kernels may be designedfor operation with CNNs as special layers, which is usually used in thefeature extraction stage of stereo matching network. However, it iscontemplated another approach may include a spherical warping layerapplied in a cost volume construction.

It is understood that machine learning algorithms may also be employedto address depth estimation by modeling the mapping between monocularimages and depth maps. Multi-task machine learning algorithm may also beemployed to jointly predict semantic labels, normals, and depthsimultaneously. For instance, a known “pano-popup” algorithm may beemployed to predict dense depth, surface normal, plane boundariessimultaneously from a single equirectangular image.

Unsupervised deep learning approaches for monocular depth estimation mayalso use self-constraints without direct depth supervision. A knownframework based on view synthesis and a loss computed when warping fromnearby views to target may be used, but such an approach may outputreconstruction loss in image construction that may look good visuallybut has a low-quality depth. To overcome known problems, a geometricconstraint may be employed. For instance, a left-right consistency andepipolar constraint may be employed. Also, for spherical images, cubemaps from 360-degree video may be employed with photometric and poseconsistency as a supervision signal. Unsupervised methods are alsounderstood as reducing the need for ground truth data, but theseexisting techniques may not produce high quality depth maps that aresatisfactory.

Also, omnidepth and mapped convolution may utilize special kernelsdesigned for spherical images to improve geometry learning accuracy.However, directly learning depth using a machine learning algorithm mayrequire a large amount of training data to learn the implicit mappingfrom 2D image space t depth. Even though 360-degree cameras can beaccessed at a reasonable cost, building a comprehensive 360-degreedataset with ground truth depth and label is not always feasible or costeffective.

While previous stereo matching approaches may perform well onperspective stereo images, they may not always be applicable directly on360-degree stereo images, due to the nature of spherical geometry. Forinstance, a known algorithm called “360SD-Net” utilizes CNN basedtechniques on 360-degree stereo images. A downside to this knownalgorithm is that it employs a learnable shifting layer for cost volumehypothesis plane sampling that tends to require extra trainingresources. It is contemplated the spherical warping layer disclosed bythe present application may be a closed-form machine learning solutionthat does not require trainable parameters. The disclosed sphericalwarping layer may also be differentiable such that it can be used inend-to-end stereo matching network.

Furthermore, prior known systems may employ a learnable shifting layerfor cost volume hypothesis plane sampling. In contrast, the disclosedtwo-stage system and method may provide a self-refining mechanism toachieve better and more accurate disparity result for 360-degree stereoimages. Moreover, RGB-D spherical data as well as spherical stereo pairsmay be expensive resources to acquire, but the disclosed two-stagemachine learning algorithm may overcome such expense due to the fact itcan be trained using a smaller dataset.

Three-dimensional (3D) scene understanding may also be relevant forapplications like virtual reality (VR), augmented reality (AR),autonomous driving, or robotics. For example, quick and reliableacquisition of omnidirectional 3D data is considered a useful buildingblock of such applications to enable user interaction with the digitalenvironment.

It is therefore contemplated that to obtain high-quality omnidirectional3D information, devices such as omnidirectional LiDARs may be used forapplications like autonomous driving vehicles or indoor 3D scans.However, LiDARs may be expensive or may produce sparse 3D scans.Compared with LiDARs, more traditional cameras may be cheaper in costand are more commonly used for capturing the visual appearance ofscenes. It is therefore contemplated that a significant cost savings canbe realized by generating high-quality omnidirectional 3D scans usingconventional camera images.

In order to realize the technological benefit and cost saving of usingconventional camera images an end-to-end two-stage depth estimation deeplearning framework (i.e., PanoDepth framework) may be used that consistsof two stages. The first stage may be a view synthesis along with astereo matching second stage for monocular omnidirectional depthestimation. The PanoDepth framework is contemplated as taking oneequirectangular projection (ERP) image as input to produce synthesizedviews in the first stage. The first stage may then pass the originalimage and one or more synthesized views to the subsequent stereomatching stage to generate finer depth map. In the stereo matchingsecond stage, an omnidirectional multi-view stereo matching network maybe used to handle omnidirectional stereo pairs.

FIG. 1 depicts an exemplary system 100 that may be used to implement thePanoDepth framework. The system 100 may include at least one computingdevices 102. The computing system 102 may include at least one processor104 that is operatively connected to a memory unit 108. The processor104 may be one or more integrated circuits that implement thefunctionality of a central processing unit (CPU) 106. It should beunderstood that CPU 106 may also be one or more integrated circuits thatimplement the functionality of a general processing unit or aspecialized processing unit (e.g., graphical processing unit, ASIC,FPGA).

The CPU 106 may be a commercially available processing unit thatimplements an instruction stet such as one of the x86, ARM, Power, orMIPS instruction set families. During operation, the CPU 106 may executestored program instructions that are retrieved from the memory unit 108.The stored program instructions may include software that controlsoperation of the CPU 106 to perform the operation described herein. Insome examples, the processor 104 may be a system on a chip (SoC) thatintegrates functionality of the CPU 106, the memory unit 108, a networkinterface, and input/output interfaces into a single integrated device.The computing system 102 may implement an operating system for managingvarious aspects of the operation.

The memory unit 108 may include volatile memory and non-volatile memoryfor storing instructions and data. The non-volatile memory may includesolid-state memories, such as NAND flash memory, magnetic and opticalstorage media, or any other suitable data storage device that retainsdata when the computing system 102 is deactivated or loses electricalpower. The volatile memory may include static and dynamic random-accessmemory (RAM) that stores program instructions and data. For example, thememory unit 108 may store a machine-learning model 110 or algorithm,training dataset 112 for the machine-learning model 110, and/or rawsource data 115.

The computing system 102 may include a network interface device 122 thatis configured to provide communication with external systems anddevices. For example, the network interface device 122 may include awired and/or wireless Ethernet interface as defined by Institute ofElectrical and Electronics Engineers (IEEE) 802.11 family of standards.The network interface device 122 may include a cellular communicationinterface for communicating with a cellular network (e.g., 3G, 4G, 5G).The network interface device 122 may be further configured to provide acommunication interface to an external network 124 or cloud.

The external network 124 may be referred to as the world-wide web or theInternet. The external network 124 may establish a standardcommunication protocol between computing devices. The external network124 may allow information and data to be easily exchanged betweencomputing devices and networks. One or more servers 130 may be incommunication with the external network 124.

The computing system 102 may include an input/output (I/O) interface 120that may be configured to provide digital and/or analog inputs andoutputs. The I/O interface 120 may include additional serial interfacesfor communicating with external devices (e.g., Universal Serial Bus(USB) interface).

The computing system 102 may include a human-machine interface (HMI)device 118 that may include any device that enables the system 100 toreceive control input. Examples of input devices may include humaninterface inputs such as keyboards, mice, touchscreens, voice inputdevices, and other similar devices. The computing system 102 may includea display device 132. The computing system 102 may include hardware andsoftware for outputting graphics and text information to the displaydevice 132. The display device 132 may include an electronic displayscreen, projector, printer or other suitable device for displayinginformation to a user or operator. The computing system 102 may befurther configured to allow interaction with remote HMI and remotedisplay devices via the network interface device 122.

The system 100 may be implemented using one or multiple computingsystems. While the example depicts a single computing system 102 thatimplements all the described features, it is intended that variousfeatures and functions may be separated and implemented by multiplecomputing units in communication with one another. The systemarchitecture selected may depend on a variety of factors.

The system 100 may implement a machine-learning algorithm 110 that isconfigured to analyze the raw source data 115. The raw source data 115may include raw or unprocessed sensor data that may be representative ofan input dataset for a machine-learning system. The raw source data 115may include video, video segments, images, and raw or partiallyprocessed sensor data (e.g., image data received from camera 114 thatmay comprise a digital camera or LiDAR). In some examples, themachine-learning algorithm 110 may be a neural network algorithm that isdesigned to perform a predetermined function. For example, the neuralnetwork algorithm may be configured in automotive applications toidentify objects (e.g., pedestrians) from images provided from a digitalcamera and/or depth map from a LiDAR sensor.

The system 100 may store a training dataset 112 for the machine-learningalgorithm 110. The training dataset 112 may represent a set ofpreviously constructed data for training the machine-learning algorithm110. The training dataset 112 may be used by the machine-learningalgorithm 110 to learn weighting factors associated with a neuralnetwork algorithm. The training dataset 112 may include a set of sourcedata that has corresponding outcomes or results that themachine-learning algorithm 110 tries to duplicate via the learningprocess. In one example, the training dataset 112 may include sourceimages and depth maps from various scenarios in which objects (e.g.,pedestrians) may be identified.

The machine-learning algorithm 110 may be operated in a learning modeusing the training dataset 112 as input. The machine-learning algorithm110 may be executed over a number of iterations using the data from thetraining dataset 112. With each iteration, the machine-learningalgorithm 110 may update internal weighting factors based on theachieved results. For example, the machine-learning algorithm 110 cancompare output results with those included in the training dataset 112.Since the training dataset 112 includes the expected results, themachine-learning algorithm 110 can determine when performance isacceptable. After the machine-learning algorithm 110 achieves apredetermined performance level (e.g., 100% agreement with the outcomesassociated with the training dataset 112), the machine-learningalgorithm 110 may be executed using data that is not in the trainingdataset 112. The trained machine-learning algorithm 110 may be appliedto new datasets to generate annotated data.

The machine-learning algorithm 110 may also be configured to identify afeature in the raw source data 115. The raw source data 115 may includea plurality of instances or input dataset for which annotation resultsare desired. For example, the machine-learning algorithm 110 may beconfigured to identify the presence of a pedestrian in images andannotate the occurrences. The machine-learning algorithm 110 may beprogrammed to process the raw source data 115 to identify the presenceof the features. The machine-learning algorithm 110 may be configured toidentify a feature in the raw source data 115 as a predeterminedfeature. The raw source data 115 may be derived from a variety ofsources. For example, the raw source data 115 may be actual input datacollected by a machine-learning system. The raw source data 115 may bemachine generated for testing the system. As an example, the raw sourcedata 115 may include raw digital images from a camera.

In the example, the machine-learning algorithm 110 may process rawsource data 115 and generate an output. A machine-learning algorithm 110may generate a confidence level or factor for each output generated. Forexample, a confidence value that exceeds a predetermined high-confidencethreshold may indicate that the machine-learning algorithm 110 isconfident that the identified feature corresponds to the particularfeature. A confidence value that is less than a low-confidence thresholdmay indicate that the machine-learning algorithm 110 has someuncertainty that the particular feature is present.

FIG. 2 illustrates a block diagram 200 illustrating an embodiment of atwo-stage framework architecture (i.e., PanoDepth) that may receive asingle ERP image as input and produces one or more high-qualityomnidirectional depth maps. As illustrated, block diagram 200 mayinclude a coarse depth estimation network 202 (i.e., first stage) and amulti-view stereo matching network 204 (i.e., second stage).

At block 206, network 202 may receive a single ERP image from camera114. For example, the ERP image may be a single 360-degree image of agiven scene. The ERP image may then be provided to a coarse depthestimation network 208 that is operable to estimate an initial depth mapthat is provided to a differentiable depth image based rendering (DIBR)module 210. Module 210 may then use the provided depth map to synthesizenovel views with pre-defined baselines.

It is contemplated that at module 208 may employ a light-weight networkto generate synthesized quality novel views, moderate quality depthmaps, or even coarse multi-plane depth maps. For instance, module 208may employ a known light-weight network called “CoordNet” for the coarsedepth estimation. The CoordNet network may be employed to utilizecoordinate convolutions to enforce 360-awareness of the ERP image.However, other known networks may be employed for the coarse depthestimation. The estimated coarse depth map and the ERP image may then beprovided to DIBR module 210 which renders multiple synthesized views ofpre-defined baselines. It is contemplated that vertical baselines may beselected and used over horizontal baselines.

By employing CoordNet, a single view 360-degree image may be passedthrough the module 208 to generate a coarse depth estimation. Thegenerated coarse depth map may support rendering the input 360-degreeimage using the DIBR module 210 which transforms pixels from sourceimage to pixels on target image in a fully differentiable manner. It iscontemplated that the transformation operation employed by DIBR modulemay be employed using a layer-structured three-dimensional sceneinference. The pixels from the source image may then be splatted on anempty target image. Occlusions may then be handled by soft z-bufferingand the final prediction may be the weighted average of points whichsplat to the same pixel.

The multi-view stereo matching network 204 (i.e., second stage) may thenbe employed to generate accurate and robust omnidirectional depthestimations. First, one or more synthesized images 212 a-212 b providedby the DIPR module 210 along with the input ERP image 206 may be passedto a stereo matching network 214 to generate a final depth map 216. Itis contemplated the stereo matching network may include two cascadedstages for disparity prediction in a coarse-to-fine manor.

Supervision from a ground truth depth 218 may also be imposed on thedepth produced from the coarse monocular depth estimation network 208and the disparity generated from stereo matching network 214. Forinstance, a ground truth depth image 218 may also be used to superviseand train the coarse depth prediction 220 generated by the coarse depthestimation network 208 and the final depth prediction 216 generated bythe stereo matching network 204 in an end-to-end fashion.

In short, block diagram 200 illustrates a two stage network thatincludes: (1) a coarse depth estimation network 208 followed by adifferentiable DIBR module 210 for novel view synthesis, and (2) amulti-view stereo matching network 204 with a differentiable SphericalWarping Layer and a cascade mechanism for efficient and high-qualitydepth estimation. The ERP image 206 may be initially passed into thecoarse depth estimation network 208 to estimate a initial depth map forDIBR module 210 to synthesize novel views with pre-defined baselines.Then the original ERP image 206 and synthesized images 212 a-212 b maybe fed into the multi-view stereo matching network 204 to generate thefinal depth map 216. These two networks may be trained in an end-to-endfashion, and both are supervised using ground truth depth 218.

FIG. 3 illustrates an embodiment of the multi-view stereo matchingnetwork 204 (i.e., second stage). As illustrated network 204 may includeone or more input levels 308 a-308 b. However, it is contemplated thatonly one input level (e.g., 308 a) may be used. Each of the input levels308 a-308 b may further include a spherical feature extraction network310 a-310 b, a spherical warping layer (SWL) 312 a-312 b, a cost volumeconstruction module 314 a-314 b, a cost aggregation module 316 a-316 b,and a depth prediction module 318 a-318 b.

As illustrated, one or more generated synthesized views (i.e., 212 a-212b) may be paired with the input ERP image 206 and passed through aweight-sharing feature extraction network 304. It is contemplatednetwork 304 may be constructed using one or more known convolutionalneural networks with multiple layers stacked together.

For instance, FIG. 4 illustrates an exemplary CNN 400 that may beimplemented as part of network 204 (or as part of other networksemployed within network 202 or network 204). As illustrated, CNN 400 mayinclude one or more convolutional layers 440-440; one or more poolinglayers 450-470; one or more fully connected layer 460; and a softmaxlayer 470. It is contemplated the CNN 400 may alternatively beimplemented using a known DNN or decision tree depending upon a givenapplication.

CNN 400 may receive data 410 (e.g., input 204 and/or synthesized views212 a-212 b). It is contemplated the data 410 may be lightly processedprior to being provided to CNN 400. Convolutional layers 440-440 may bedesigned to extract features from data 410. For instance, convolutionallayer 440-440 may employ filtering operations (e.g., kernels) beforepassing on the result to the next layer of the CNN 400. The filteringoperations may include image identification, edge detection of an image,and image sharpening that are applied when the data 410 received is animage.

The CNN 400 may also include one or more pooling layers 450-470 thatreceives the convoluted data from the respective convolution layer440-440. Pooling layers 450-470 may include one or more pooling layerunits that apply a pooling function to one or more convolution layeroutputs computed at different bands using a pooling function. Forinstance, pooling layer 450 may apply a pooling function to the kerneloutput received from convolutional layer 440. The pooling functionimplemented by pooling layers 450-470 may be an average or a maximumfunction or any other function that aggregates multiple values into asingle value.

Next, one or more fully connected layers 480 may attempt to learnnon-linear combinations for the high-level features in the output datareceived from the convolutional layers 440-440 and pooling layers450-470. Lastly, CNN 400 may include a softmax layer 490 that combinesthe outputs of the fully connected layer 480 using softmax functions.The CNN 400 may employ a batch normal layer, a max pooling layer, and adropout layer. It is contemplated CNN 400 may employ spatialpyramid-pooling layer to extract multi-scale context information. It isalso contemplated CNN 400 may include one or more pooling layers havingvarying sizes.

With reference back to FIG. 3, the multi-scale context information maythen be input to the spherical feature network 310 a-310 b. It iscontemplated that for each input in the stereo pair with a resolution of3×Z×W, the feature extraction network 310 a-310 b may output a featuremap having a resolution of

${32 \times \frac{H}{4} \times \frac{W}{4}}.$

It is also contemplated that for network 310 a-310 b, each cascade level(l^(th)) where l>1 the output feature map may have a resolution of

$32 \times \frac{H}{2^{n - 1}} \times {\frac{W}{2^{n - 1}}.}$

However, it is contemplated that the feature map may have a resolutiongreater or less than 32.

Again, over the last several years there has been a significant growthin the VR and AR market. As a result of this growth, a larger number of360-degree cameras are being developed and used as a source of contentgeneration for VR and AR applications. By pairing two adjacent360-degree images, it is contemplated that stereo matching techniquesmay be leveraged to generate 3D information. However, sinceequirectangular projection (ERP) introduces distortions in the image(e.g., image 206) previous stereo matching approaches (e.g.,conventional and deep learning machine algorithms) may not be applicableto ERP stereo pairs.

It is also contemplated that for perspective stereo images, disparitymay also be proportional to the inverse depth. The discrete disparityhypothesis planes could be sampled uniformly and later merged togetherbased on estimated probabilities. For spherical stereo, however,disparity may be related to both inverse depth and latitude valuesacross the image. With the irregular distortion introduced by sphericalgeometry, uniform hypothesis plane sampling is not ideal forequirectangular stereo pairs. As discussed above, known algorithms tryto employ a trainable shifting filter to select the optimal hypothesisstep, but these approaches require large computational processingoverhead and converge at an unacceptably slow rate.

Network 204 may therefore include one or more spherical warping layers(SWL) 312 a-312 b that operably transform the uniformly sampleddisparity or inverse depth to spherical coordinates during a sphericalcost volume construction. It is contemplated the SWL 312 a-312 b may bedifferentiable and may be used (e.g., as a plug in) within network 204for end-to-end deep stereo matching networks. SWL 312 a-312 b mayprovide stereo matching approaches for perspective projection imagesthat are applicable to ERP stereo pairs. It is contemplated that SWL 312a-312 b may deterministically transform uniformly sampled inverse depthor disparities to spherical displacement to reduce processing needs ormemory usage. The SWL 312 a-312 b may therefore be used instead of alearnable layer for constructing a cost volume.

For instance, SWL 312 a-312 b may be employed as part of an inversedepth that is sampled uniformly to cover the whole depth range, asrepresented by Equation 1 below:

$\begin{matrix}{{\frac{1}{d_{j}} = {\frac{1}{d_{\max}} + {\left( {\frac{1}{d_{\min}} - \frac{1}{d_{\max}}} \right)\frac{vxj}{D - 1}}}},{j \in {D - 1}}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

Where D is the total number of hypothesis planes, d_(j) is the j^(th)depth plane, d_(min) and d_(max) are the minimum and maximum value ofdepth, and v is the plane interval. It is contemplated that SWL 312a-312 b may transform depth hypothesis d_(j) to displacement inspherical domain C_(j) to map pixels from the synthesized view to theoriginal view. The displacement C_(j) may then be defined using equation2 below:

$\begin{matrix}{{C_{x,y} = 0},{C_{y,j} = {\frac{{\cos(\theta)}xb}{d_{j}}\frac{H_{f}}{\pi}}}} & {{Equation}\mspace{14mu}(2)}\end{matrix}$

Where θ refers to latitudinal values across the image, b represents thebaseline, and H_(f) is the height of the feature map. As opposed toknown learnable shifting filters, SWL 312 a-312 b is designed to be aclosed-form solution that does not require overhead training.

It is contemplated that with the displacements Cj from SWL 312 a-312 b,the spherical features extracted from M views may be aggregated to buildthe cost volume with uniformly sampled depth hypothesis. Known fusionimplementations that include a variance-based cost volume formationmethod or cascade design may also be applied to improve accuracy. It iscontemplated that SWL 312 a-312 b may be designed to work seamlesslywith such known cascaded designs. Also, at each level l, the depthhypothesis may be uniformly sampled using new intervals calculated basedon predictions in level l+1. The corresponding displacements may then becalculated using the same spherical coordinate mapping procedure.

Network 204 may further include a cost volume construction module 314a-314 b which may use the extracted feature maps to build a cost volume.The feature maps may be provided from the spherical feature extractionmodule 310 a-310 b or from the spherical warping layer 312 a-312 b whenimplemented.

After the construction of cost volume employed by module 316 a-316 b, acost aggregation module 316 a-316 b may be employed to aggregatedifferent levels of spatial context information using an hourglassshaped encoding and decoding process. Module 316 ba-316 b may bedesigned using one or more multi-scale 3-Dimensional CNN machinelearning algorithms. It is also contemplated that module 316 a-316 b mayhelp to regularize noises in ambiguous regions caused by occlusions ortexture-less surfaces to help improve final prediction quality. Module316 a-316 b may then regress disparity value pixel-wise for each stage 1as shown by Equation 3 below:

$\begin{matrix}{\frac{1}{\overset{\_}{d}} = {\frac{1}{d_{\min}}\left( {\frac{1}{d_{\max}} - \frac{1}{d_{\min}}} \right)\frac{k}{D - 1}}} & {{Equation}\mspace{14mu}(4)}\end{matrix}$

where k is the summation of each plane level l weighted by itsnormalized probability as shown by Equation 4 below:

k=Σ _(j=0) ^(D−1)σ(p _(j))×v _(i,l) ×j  Equation (4)

where σ(⋅) represents softmax functions and p_(j) denotes theprobability of j^(th) plane value. v_(j,l) is the interval at the levell.

It is contemplated that network 200 may be trained in an end-to-endfashion where supervision may be applied on both sub-processes (i.e.stage 202 and stage 204). The final loss function for the completenetwork may be defined as Loss=λ₁L_(coarse)+λ₂L_(stereo) where λ₁ and λ₂are the weights of coarse depth estimation loss and stereo matching lossrespectively. It is also contemplated the combination of smooth L₁ lossand a smoothness term for depth estimation on non-empty pixels denotedas p, depth is denoted as D in Equation 5 below:

$\begin{matrix}{L_{coarse} = {\frac{\propto}{M}{\sum_{p}{{M(P)}{{{D_{gt}(P)} - {D_{pred}(p)}}}\frac{\beta}{M}{\sum_{p}{{M(p)}{{\nabla{D_{pred}(p)}}}^{2}}}}}}} & {{Equation}\mspace{14mu}(5)}\end{matrix}$

Where M(p) is a binary mask that is used to mask out missing regions, αand β are the weights for L₁ loss and smoothness term. It is alsocontemplated that network 200 may calculate berHu loss on all outputsfrom each level and then compute the weighted summation. The same binarymask M may be applied to the complete network 200 and the stereomatching loss may be defined using Equation 6 below:

$\begin{matrix}{L_{stereo} = {\frac{1}{M}{\sum_{i \in M}{\sum_{l}^{N}{\lambda_{l}{L_{berHu}\left( {D_{gt},} \right)}}}}}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

Where λ_(l) is the loss weight for l^(th) level.

FIGS. 5-7 illustrate various applications that may be used forimplementation of the two-stage network (i.e., network 202 and 204). Forinstance, FIG. 5 illustrates an embodiment in which a computing system540 may be used to control an at least partially autonomous robot, e.g.an at least partially autonomous vehicle 500. The computing system 540may be like the system 100 described in FIG. 1. Sensor 530 may compriseone or more video/camera sensors and/or one or more radar sensors and/orone or more ultrasonic sensors and/or one or more LiDAR sensors and/orone or more position sensors (like e.g. GPS). Some or all these sensorsare preferable but not necessarily integrated in vehicle 500.

Alternatively, sensor 530 may comprise an information system fordetermining a state of the actuator system. The sensor 530 may collectsensor data or other information to be used by the computing system 540.One example for such an information system is a weather informationsystem which determines a present or future state of the weather inenvironment. For example, using input signal x, the classifier may forexample detect objects in the vicinity of the at least partiallyautonomous robot. Output signal y may comprise an information whichcharacterizes where objects are located in the vicinity of the at leastpartially autonomous robot. Control command A may then be determined inaccordance with this information, for example to avoid collisions withsaid detected objects.

Actuator 510, which may be integrated in vehicle 500, may be given by abrake, a propulsion system, an engine, a drivetrain, or a steering ofvehicle 500. Actuator control commands may be determined such thatactuator (or actuators) 510 is/are controlled such that vehicle 400avoids collisions with said detected objects. Detected objects may alsobe classified according to what the classifier deems them most likely tobe, e.g. pedestrians or trees, and actuator control commands A may bedetermined depending on the classification.

Shown in FIG. 6 is an embodiment in which computer system 640 is usedfor controlling an automated personal assistant 650. Sensor 630 may bean optic sensor, e.g. for receiving video images of a gestures of user649. Alternatively, sensor 630 may also be an audio sensor e.g. forreceiving a voice command of user 649.

Control system 640 then determines actuator control commands A forcontrolling the automated personal assistant 650. The actuator controlcommands A are determined in accordance with sensor signal S of sensor630. Sensor signal S is transmitted to the control system 640. Forexample, classifier may be configured to e.g. carry out a gesturerecognition algorithm to identify a gesture made by user 649. Controlsystem 640 may then determine an actuator control command A fortransmission to the automated personal assistant 650. It then transmitssaid actuator control command A to the automated personal assistant 650.

For example, actuator control command A may be determined in accordancewith the identified user gesture recognized by classifier. It may thencomprise information that causes the automated personal assistant 650 toretrieve information from a database and output this retrievedinformation in a form suitable for reception by user 649.

In further embodiments, it may be envisioned that instead of theautomated personal assistant 650, control system 640 controls a domesticappliance (not shown) controlled in accordance with the identified usergesture. The domestic appliance may be a washing machine, a stove, anoven, a microwave or a dishwasher.

Shown in FIG. 6 is an embodiment in which computing system controls anaccess control system 600. Access control system may be designed tophysically control access. It may, for example, comprise a door 601.Sensor 630 is configured to detect a scene that is relevant for decidingwhether access is to be granted or not. The sensor 630 may collect imagedata or video data related to the scene. It may for example be anoptical sensor for providing image or video data, for detecting aperson's face. Classifier may be configured to interpret this image orvideo data e.g. by matching identities with known people stored in adatabase, thereby determining an identity of the person. Actuatorcontrol signal A may then be determined depending on the interpretationof classifier, e.g. in accordance with the determined identity. Actuator610 may be a lock which grants access or not depending on actuatorcontrol signal A. A non-physical, logical access control is alsopossible.

Shown in FIG. 7 is an embodiment in which computing system 740 controlsa surveillance system 700. This embodiment is largely identical to theembodiment shown in FIG. 5. Therefore, only the differing aspects willbe described in detail. Sensor 730 is configured to detect a scene thatis under surveillance. The sensor 730 may collect image data or videodata related to the scene. The computing system does not necessarilycontrol an actuator 710, but a display 710 a. For example, the machinelearning system may determine a classification of a scene, e.g. whetherthe scene detected by optical sensor 730 is suspicious. Actuator controlsignal A which is transmitted to the display 710 a may then e.g. beconfigured to cause the display 710 a to adjust the displayed contentdependent on the determined classification, e.g. to highlight an objectthat is deemed suspicious by machine learning system.

The processes, methods, or algorithms disclosed herein can bedeliverable to/implemented by a processing device, controller, orcomputer, which can include any existing programmable electronic controlunit or dedicated electronic control unit. Similarly, the processes,methods, or algorithms can be stored as data and instructions executableby a controller or computer in many forms including, but not limited to,information permanently stored on non-writable storage media such as ROMdevices and information alterably stored on writeable storage media suchas floppy disks, magnetic tapes, CDs, RAM devices, and other magneticand optical media. The processes, methods, or algorithms can also beimplemented in a software executable object. Alternatively, theprocesses, methods, or algorithms can be embodied in whole or in partusing suitable hardware components, such as Application SpecificIntegrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs),state machines, controllers or other hardware components or devices, ora combination of hardware, software and firmware components.

While exemplary embodiments are described above, it is not intended thatthese embodiments describe all possible forms encompassed by the claims.The words used in the specification are words of description rather thanlimitation, and it is understood that various changes can be madewithout departing from the spirit and scope of the disclosure. Aspreviously described, the features of various embodiments can becombined to form further embodiments of the invention that may not beexplicitly described or illustrated. While various embodiments couldhave been described as providing advantages or being preferred overother embodiments or prior art implementations with respect to one ormore desired characteristics, those of ordinary skill in the artrecognize that one or more features or characteristics can becompromised to achieve desired overall system attributes, which dependon the specific application and implementation. These attributes caninclude, but are not limited to cost, strength, durability, life cyclecost, marketability, appearance, packaging, size, serviceability,weight, manufacturability, ease of assembly, etc. As such, to the extentany embodiments are described as less desirable than other embodimentsor prior art implementations with respect to one or morecharacteristics, these embodiments are not outside the scope of thedisclosure and can be desirable for particular applications.

What is claimed is:
 1. A method for employing a spherical warping layermachine learning algorithm within a spherical stereo matching network,comprising: receiving one or more equirectangular projection (ERP)images from a sensor; receiving a feature map from a spherical featureextraction machine learning algorithm; and transforming an inverse depthhypothesis to a displacement in a spherical-coordinate domain, whereinthe displacement is generated using a cosine angle of one or morelatitudinal values across the one or more ERP images, one or morebaseline values, and a height of the feature map.
 2. The method of claim1, wherein the inverse depth hypothesis covers a whole depth range. 3.The method of claim 1, further comprising: mapping one or more pixelsfrom one or more synthesized images to the ERP image.
 4. The method ofclaim 3, wherein the spherical stereo matching network includes twocascaded stages for disparity prediction in a coarse-to-fine manner,wherein a multi-view stereo matching machine learning algorithm isoperable to generate a final spherical depth map.
 5. The method of claim4, wherein the spherical stereo matching network further includes aspherical feature extraction algorithm operable to pair the one or moresynthesized images with the ERP image.
 6. The method of claim 5, whereinthe spherical stereo matching network generates one or more featuremaps.
 7. The method of claim 6, wherein the one or more feature mapshave a resolution of 32 multiplied by one fourth of a width of the ERPimage and one fourth of a second height of the ERP image.
 8. The methodof claim 6, wherein the spherical stereo matching network furtherincludes a cost volume construction algorithm that aggregates sphericalfeatures extracted from the ERP image and the one or more synthesizedimages.
 9. The method of claim 8, wherein the cost volume constructionalgorithm generates a cost volume using a depth hypothesis that isuniformly sampled.
 10. The method of claim 9, wherein the one or morefeature maps are used by the cost volume construction algorithm togenerate the cost volume.
 11. The method of claim 9, wherein the depthhypothesis is uniformly sampled at a specified level using newintervals.
 12. The method of claim 10, wherein the spherical stereomatching network further includes a cost aggregation machine learningalgorithm operable to aggregate the cost volume using one or more3-dimensional convolutional neural networks.
 13. The method of claim 12,wherein the cost aggregation machine learning algorithm is implementedusing an hourglass encoding and decoding processes.
 14. The method ofclaim 12, wherein the spherical stereo matching network further includesa regression algorithm that regresses a disparity value pixel-wise foreach specified level.
 15. A system for employing a spherical warpinglayer machine learning algorithm within a spherical stereo matchingnetwork, comprising: a sensor operable to capture one or moreequirectangular projection (ERP) images; a controller operable to:receive a feature map from a spherical feature extraction machinelearning algorithm; and transform an inverse depth hypothesis to adisplacement in a spherical-coordinate domain, wherein the displacementis generated using a cosine angle of one or more latitudinal valuesacross the one or more ERP images, one or more baseline values, and aheight of the feature map.
 16. The system of claim 15, wherein theinverse depth hypothesis covers a whole depth range.
 17. The system ofclaim 15, further comprising: mapping one or more pixels from one ormore synthesized images to the ERP image.
 18. A method for employing aspherical warping layer machine learning algorithm within a sphericalstereo matching network, comprising: receiving one or moreequirectangular projection (ERP) images from a sensor; receiving afeature map from a spherical feature extraction machine learningalgorithm; transforming a sampled disparity to a displacement in aspherical-coordinate domain, wherein the displacement is generated usinga cosine angle of one or more latitudinal values across the one or moreERP images, one or more baseline values, and a height of the featuremap; and configuring a physical system to operate using the displacementin the spherical-coordinate domain.
 19. The method of claim 18, furthercomprising: transforming an inverse depth hypothesis to the displacementin the spherical coordinate domain, wherein the inverse depth hypothesiscovers a whole depth range.
 20. The method of claim 18, furthercomprising: mapping one or more pixels from one or more synthesizedimages to the ERP image.